The geometric phase has by now a considerable history, and many
generalizations have been done. One well-known
extension [1]} is the application to systems in which
degeneracies originating from symmetry exist, for example, if
time-reversal symmetry leads to Kramers doublets [2]}.
In this case the integral defining the geometric phase becomes the
Wilson loop, and the geometric phase itself becomes an \(SU(2)\)  matrix
(a quaternion). The adiabatic loop is of particular interest if it
encircles crossing points between Kramers doublets. We are confident
that our ideas are applicable to these types of more complex
scenarios.
